1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
9966 [12]
2 years ago
6

Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less

than the sum if the other two
Mathematics
1 answer:
Sergio039 [100]2 years ago
4 0

Answer:

The shortest side of the triangle is 18

Step-by-step explanation:

Let the sides the triangle be x, y and z.

From the question, the perimeter of the rectangle is 64, that is

x + y + z = 64 ...... (1)

Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)

The third side, z, is 20 less than the sum of the other two, that is

z + 20 = x + y ...... (3)

Substitute equation (3) into (1)

Then,

z + 20 + z = 64

2z +20 = 64

2z = 64 - 20

2z = 44

z = 44/2 k

z = 22

From equation (3)

z + 20 = x + y

Then, k

22 + 20 = x +y

42 = x + y

x = 42 - y ...... (4)

Substitute this into equation 2

3x = 4y

3(42-y) = 4y

126 - 3y = 4y

4y + 3y = 126

7y = 126

y = 126/7

y = 18

Substitute this into equation (4)

x = 42 - y

x = 42 - 18

x = 24

∴ x = 24, y = 18 and z = 22

Hence, the shortest side of the triangle is 18.

You might be interested in
WANT POINTS JUST ANSWER THIS CORRECTLY FOR 45!!!
Lelu [443]
Since we’re trying to find minutes, concert all known information to minutes

1 hr 15 mins = 75 mins
1 hr 30 mins = 90 mins

Next, calculate how many total minutes Gage has skated in the first 8 days

75(5) + 90(3) = 645 mins

Create an equation to find the average of Gage’s minutes of skating. Add up all the minutes and divide by the total amount of days and set equal to 85, the average we are trying to get.

(645 mins + x mins)/9 days = 85

Solve for x

645 + x = 765
x = 120

So, in order to have an average of an 85 minute skate time, Gage would need to skate 120 minutes on the ninth day.
3 0
2 years ago
Need help , if you can answer it pls do . thank you
lara [203]

Answer:

9

Step-by-step explanation:

14-5=9

therefore TV=9

hope this helped

3 0
3 years ago
The volume of a rectangular prism is 720in cubes if the area of the base is 90 in find it's height draw and label a model to sho
Dmitriy789 [7]
Do 720 divided by 90 and then draw 7 100 base blocks 2 ten blocks and tjen divide 9 10 blocks! hope that helped
5 0
3 years ago
Read 2 more answers
Find the perimeter and area
stepladder [879]

Answer:

32 times square root of 3.  is the perimeter, area is 48 times square root of 3

Step-by-step explanation:

4 0
3 years ago
Complete the proof by providing the missing statement and reasons
Lisa [10]

Answer:

In triangle SHD and triangle STD.

\overline{SD} \perp \overline{HT}          [Side]

Since, a line is said to be perpendicular to another line if the two lines intersect at a right angle.

⇒ \angle SDH = \angle SDT = 90^{\circ}

\overline{SH} \cong \overline{ST}       [leg]               [Given]

Reflexive property states that the value is equal to itself.

\overline{SD} \cong \overline{SD}       [Leg]       [Reflexive property]

HL(Hypotenuse-leg) theorem states that any two right triangles that have a congruent hypotenuse and a corresponding congruent leg are the congruent triangles.


then, by HL theorem;

\triangle SHD \cong \triangle STD                       Proved!



6 0
3 years ago
Other questions:
  • A sector of a circle has a central angle of 80°. If the circle has a radius of 5.5 inches,what is the area of the sector? (pi =
    10·1 answer
  • Which of the following statements are equivalent to the statement "price increased by 100%"?
    9·1 answer
  • dieon has 3/4 pound of dog treats he will give his dog 1/8 of treats everyday how long will the bag last
    13·1 answer
  • Which of the following qualities does not describe a line? Select all that apply.
    11·2 answers
  • determine whether y varies directly with x. if so find the constant variation and write the equation x -6, -9, -15; y 2, 3, 5
    7·2 answers
  • Help pls lol dont answer if you dont know thankyou <3
    15·2 answers
  • The height h is greater than 2.5 meters.<br> Write an inequality for the word sentence
    7·1 answer
  • 23.79 ÷3 in long divison​
    9·2 answers
  • Over a 5-hour period, the
    10·1 answer
  • PLEASE HELP! <br><br> will give brainlist
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!